Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✶� ✁✂✄☎✆✄✝✞✟ ✠✂✡✟✝✞☛✡☞

❊✌✍✎❝✏✑✍ ✒✓

✹ ✥

✤ ✔

✤ ✔

✢ ✕ ✛

✢ ✕ ✕ ✛

✢ ✕ ✛

② ✖ ✖

✖

✖

✻ ✗✗

✸ ✘ ✗✗

✸ ✙

✷

✷

✷

❜ ▼✐✚✐✜✉✜ ✣✦❧✉❡ ✧❢ ★ ✐s ✩✪

✺ ✥ ▼✐✚✐✜✉✜ ✦t ✫✬✭ ✮✯✰ ✱ ✲ ✳✴ ✵ ①✼ ✽✾ ✿❀

❙✧ ❛ ❁ ❂✬✭ ❃ ❁ ✮

❜ ❈✉❄✣❡ ❅✦ss❡s t❤❄✧✉❆❤ ✫❇✭ ❇❉✯✭ s✧s✉❋st✐t✉t✐✚❆ ● ❁ ❇ ✦✚❞ ★ ❁ ❇❉ ✐✚t✧

❍ ■❏ ❑ ▲◆ ❖ P ◗ ❘❚

❯

❱ ❲❳ ❨ ❩

❳

❳

❬

❬

❬

❭❪ ❭ ❫ ❴

❵ ❪

❣

❥

❦ ✥

♠ ♥

♠ ♥

♠ ♥

♦ ♣ q ♦r✈ ✇③ ♣

q ♦ ♣r✈

✇③ ♣

q ♦ ♣ ♣

q ♦ ♣

④ ④ ④ ④

④

④

④

⑤ ⑥ ⑦ ⑤ ⑤ ⑦

⑤ ⑦ ⑦ ⑦

⑤ ⑦ ⑤ ⑦

⑤ ⑦ ⑧

⑨ ⑨

⑨

⑨

⑨

❜ ⑩✐✚❡ ✧❢ s❶✜✜❡t❄❶ ✐s ● ❁ ❂❇

❷

❸ ❹

❸ ❹

❸ ❹

❺ ❻ ❼

❺ ❻ ❼

❺ ❼

❺ ❼

❺ ❼ ❽

❼ ❻ ❽

❾ ❾

❾

❾

❾

❾

❾

❿ ➀ ➁ ➂

❿ ➁ ➃ ➂

❿ ➁ ➃

➁➃

❿

➁➃

❿

➁➃

❿

➄

➄

➄

➄

❊✌✍✎❝✏✑✍ ✒➅

✹ ✥ ➆ ➇➆ ➇➈ ➉ ➊ ➉ ➈➋ ➋ ➋ ➋➌ ➍ ➎➌ ➌ ➏ ➐➑

❜ ➒❡ ❆❄✦❅❤ ➓❄✧ss❡s t❤❡ ●➔✦→✐s ➣❤❡❄❡★ ❁ ↔✭ ✐✪❡✪ ➣❤❡❄❡ ↕ ➙ ➛➜ ➜➝ ➞ ➟➝ ➠➡ ❯

➢ ➤➢ ➤

➥ ➦ ➧

➦ ➥ ➧

➦ ➧ ➧ ➧

➧ ➧ ➦

➨ ➨

➨ ➨

➨ ➨

➨ ➨

➩ ➫ ➭➩ ➯

➩ ➲ ➳ ➯

➩ ➲ ➯ ➵➸ ➳ ➯

➲

➩➵➸ ➳

➺

❙✧ t❤❡ ✐✚t❡❄s❡➓t✐✧✚s ➣✐t❤ t❤❡ ●➔✦→✐s ✦❄❡

✦t ➻➼➽

➾➚➪

➶

➹➘ ➴ ✦✚❞ ✫❂❉✭ ↔✯✪

✺

➷ ➬➷ ➬

➮

➱ ✃ ➮ ❐

✃ ❐ ➮

❒ ❮ ❰ ❰

❮❰ ❮❰ ❮

ÏÐÐÑÒ ÓÑ Ô ÓÕÖ ×

× Ô

Ø ÙÚÛ

❙✧ Ü ❁ ❂❇↔❛ ✦✚❞ ❃ ❁ ✬❛✪

★➔✐✚t❡❄➓❡❅t ✦t ✬ ✰Ü ❁ ✬

Ý

Ý

Þ ßà

Þ

ßà

á â ã

â ã

✦✚❞ ä åæçè

éêëä åì í

í

îï

ð

îï

❊✌✍✎❝✏✑✍ ✒ñ

✺ ✬●ò ❁ ❉● ó ❇ô✬●ò ❂ ❉● ❂ ❇ ❁ ↔õs✐✚❆ t❤❡ ö✉✦❞❄✦t✐➓ ❢✧❄✜✉❧✦ ➣✐t❤ ❛ ❁ ✬✭❃ ❁ ❂❉ ✦✚❞ Ü ❁ ❂❇❯

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

❚♦�✁✂ ✄☎ ❚✆✝ ✞✟✠✡☛✠☞✁✂ ✌♦☛♠✟✍✠ ✠✎✡ ☞✆✝ ✡✁✏✂☛✁♠✁✎✠✎☞✷

✤✣ ✣ ✢ ✣ ✣ ✑ ✑ ✣

✑①

✭ ✒✮ ✭ ✒✮ ✒ ✹ ✭ ✓✮

✔ ✹

✕

✤✢

✤✢

✒ ✔✽

✻

✔ ✖

✹

✗ ✘❡ ✙✚s❝✛✚✐✚✜❛✜t ✥✚t❤ ✦ ✧ ★✩ ❜ ✧ ✪ ❛✜✙

✫✬✶

✶✯✚s

✰ ✱ ✲

✱ ✲ ✳ ✳

✱

✴ ✵✸✺

✼ ✺ ✺✼

✼✾

✿

❀

❀

❙❁ t❤❡✛❡ ✚s ❁✜❧② ❁✜❡ ✛❁❁t✩ ✚❂❡❂ t❤❡ ❃❡✛t❡❄

❧✚❡s ❁✜ t❤❡ ❅❆❛❄✚s❂

❇ ❊q✉❛❧ ✛❁❁ts ✥❤❡✜ ✙✚s❝✛✚✐✚✜❛✜t ✚s ❈❡✛❁❉

❋ ● ❍ ●

❍ ❍ ■ ■ ●

❍ ●

●

● ❏

❑ ▲▼

◆ ◆

◆

◆

◆

❖ P

◗ ❖❘ ❖ ❯ P

❱❲ ❳ P

❯

❯

❨

❨

❨

❨

❩ ❬❛✜❣❡✜t t❁ t❤❡ ❅❆❛❄✚s ✚✐♣❧✚❡s ❡q✉❛❧ ✛❁❁ts✩

s❁ ✙✚s❝✛✚✐✚✜❛✜t ✚s ❈❡✛❁❉

❭ ❪ ❭ ❪❫ ❴

❵ ❞ ❢ ❞

❥ ❢ ❦ ❢ ❦ ❢ ❞

❥ ❥ ❢ ❞

❢ ❥ ❞

❞♥ ❢ ❦ ❦

❦

❞♥

❞ ♥

r ✈✇

③ ③

③ ③ ③

③ ③

③

④ ⑤

⑥ ⑦ ④ ⑧ ④ ⑤

④ ④ ⑦ ④⑨ ⑤

④ ④④ ⑦ ⑤

④④ ④④ ④ ④ ⑦

⑥ ④

④④ ⑦⑩⑥⑤

⑨

⑦⑦

⑥⑧⑤

❶

❶

❶

❶

❶

❷ ❸❁ ✛❡❛❧ s❁❧✉t✚❁✜s ✥❤❡✜ ✙✚s❝✛✚✐✚✜❛✜t ❹ ❺ ❻❉

❼ ❽

❾ ❿

❾ ❾ ➀ ➀ ❿

❾ ❿

➁

➂ ➃➄

➅

➅

➅

➆ ➇

➈ ➆ ➉ ➊ ➇

➋➈ ➌ ➇

➍

➊

➎

➎

➏➐ ➑❁✛ ❛ q✉❛✙✛❛t✚❝ t❁ ➒❡ ✜❁✜❆✜❡❣❛t✚❃❡ ➓➔❻→

➣❁✛ ❛❧❧ ❅✩ ✚t ✐✉st ❤❛❃❡ ❛t ✐❁st ❁✜❡ ✛❁❁t✩ s❁

❹ ↔ ❻ ❛✜✙ ✦ ↕ ❻❂

➙ ➛ ➙ ➛

➜ ➝

➜ ➜ ➞ ➞ ➜ ➝

➜ ➟ ➝

➠

➡ ➢➤

➤

➤

➤

➥ ➦

➧ ➥ ➨ ➨ ➩ ➦

➫ ➩➭ ➯ ➦

➩➲

➩➭

➳

➳

➵➸➺➺➻➼➽

➾➚➪➶ ➪➹➘➪ ❹ ↔ ➴ ➷➬ ➮➚➪ ➬➱✃❐❒➷➶➮➪ ➷➮ ❮➶➮➶❰➘Ï

✃➚❰ ➘ Ð➱➘Ñ❰➘➪➷❒ ➪➚ Ò➶ ➮➚➮Ó➮➶❮➘➪➷Ô➶Õ Ö➹➶

❒➚➮Ñ➷➪➷➚➮ × Ø ➴ ➷➬ ➘Ï➬➚ ➮➶❒➶➬➬➘❰Ù ➪➚

➶➮➬➱❰➶ ➪➹➘➪ ➪➹➶ Ð➱➘Ñ❰➘➪➷❒ ➹➘➬ ➘ Ú➚➬➷➪➷Ô➶

➬➹➘Ú➶ Û➚Ú➶➮➷➮❮ ➱ÚÜ➘❰ÑÝ ❰➘➪➹➶❰ ➪➹➘➮ ➘

➮➶❮➘➪➷Ô➶ ➬➹➘Ú➶ Û➚Ú➶➮➷➮❮ Ñ➚Ü➮Ü➘❰ÑÝÞ ➬➚

➪➹➘➪ ➪➹➶ ❒➱❰Ô➶ ❰➶ß➘➷➮➬ ➘Ò➚Ô➶ ➪➹➶ àÓ➘á➷➬

➘➮Ñ ➮➶Ô➶❰ ❮➚➶➬ Ò➶Ï➚Ü ➷➪Þ ➘➬ Ü➚➱ÏÑ Ò➶ ➪➹➶

❒➘➬➶ ➷✃ × â ➴Õ ã➮ ➪➹➷➬ Ð➱➶➬➪➷➚➮ × Ü➘➬ ❮➷Ô➶➮

➘➬ Ú➚➬➷➪➷Ô➶ ÛäÝÞ ➬➚ Ü➶ Ñ➷Ñ ➮➚➪ ➮➶➶Ñ ➪➚ ➱➬➶

➪➹➷➬ ❒➚➮Ñ➷➪➷➚➮ ➘➪ ➘ÏÏÕ

➏➏ ➑❁✛ ❛ q✉❛✙✛❛t✚❝ t❁ ➒❡ ✜❡❣❛t✚❃❡ ➣❁✛ ❛❧❧ ❅✩

✚t ✐✉st ❤❛❃❡ ✜❁ ✛❡❛❧ ✛❁❁ts✩ s❁ ❹ ❺ ❻ ❛✜✙

✦ ❺ ❻❂

å æ

å ç ç å æ

è æ

æ å

é êë

ì

ì

ì

í î

ï í ð íñ î

ò óô î

ò

óô

õ

õ

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✸✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛

☞✌✍✍✎✏✑

❚✒✓ ✔✕✖✗✘✙✘✕✖ ❛ ✤ ✚ ✓✖✛✜✢✓✛ ✙✒✣✙ ✙✒✓❢✜✖✔✙✘✕✖ ✘✛ ✖✓✥✣✙✘✦✓ ✛✒✣✧✓✗ ✣✖✗ ✙✒✓✢✓❢✕✢✓✢✓r✣✘✖✛ ★✓✩✕✪ ✙✒✓ ①✲✣✫✘✛✬ ✭✖ ✙✒✘✛ ✔✣✛✓❛ ✮ ♠✱ ✣✖✗ ✘✙ ❢✕✩✩✕✪✓✗ ❢✢✕r ✙✒✓ ✔✕✖✗✘✙✘✕✖✕✖ ✯ ✙✒✣✙ ❛ ✤ ✚✱ ✣✛ ✛✓✓✖ ✘✖ ✙✒✓ ✣✖✛✪✓✢✬

✰✳ ✴❡ ✵✇♦ ✷❡✹♦s ♦✺ ✻ ✻✼✽ ❜✽ ❝✾ ✿✹❡

❀ ❁ ❀❂ ❂ ❃❄

❃

❅

❆

❇✿❈❞

❉ ❉ ❉❊ ❊ ❋●

❋

❍

■

❏❑

✴❡ ▲♦s✐✵✐✈❡ ❞✐▼❡✹❡❈◆❡ ❖❡✵✇❡❡❈ ✵❤❡s❡✷❡✹♦s ✐s

P ◗ PPP P P

❘P

❘P

❙ ❙ ❯❱

❯

❙ ❙ ❯❱

❯

❙ ❯❱

❯

❙ ❯❱

❯

❲

❳

❲

❳

❳ ❲

❳

❲

❨ ❨ ❨

❨

❩♦❬ ✐❈ ✵❤✐s ◆✿s❡❬

❭❪

❭ ❪

❪

❪ ❫

❦

❦

❦

❦

❴❵

❴❣❥

❴❵ ❣❥

❧❴

❥

♥

♥

♥

☞✌✍✍✎✏✑

♣✕✙✓ ✙✒✣✙ r✕✗✜✩✜✛ ✛✘✥✖✛ ✪✓✢✓ ✜✛✓✗ ✘✖✙✒✓ ✥✓✖✓✢✣✩ ✓✫✧✢✓✛✛✘✕✖ ❢✕✢ ✙✒✓ ✧✕✛✘✙✘✦✓✗✘✛✙✣✖✔✓✱ ✣✛ ❛ ✔✕✜✩✗ ★✓ ✖✓✥✣✙✘✦✓✬ q✓✢✓❛ ✮ t ✣✖✗ ✛✕ ✙✒✓ r✕✗✜✩✜✛ ✪✣✛ ✖✕✙ ✢✓✉✜✘✢✓✗✘✖ ✙✒✓ ✛✧✓✔✘②✔ ✔✣✛✓ ✘✖ ✙✒✘✛ ✉✜✓✛✙✘✕✖✬

③④⑤⑥⑦⑧⑨⑤ ⑩③

❶ ❷ ❸

❷ ❸

❹ ❺

❹ ❺

❻ ❼❽❾

❿ ❼➀❾

➁ ➂

➂

❩➃❖s✵✐✵➃✵✐❈➄ ➅➆➇ ✐❈✵♦ ➅➈➇➉

➊ ➋ ➊➌ ➌➍ ➎➏

➐ ➑➐ ➑

➒ ➊ ➋

➊ ➒ ➋

➋ ➋ ➊

➌ ➌

➌ ➌

➌ ➌

➓➔ →

➣ ➍ →

➣ ↔↕ ➍

➏

❩➃❖s✵✐✵➃✵✐❈➄ ✐❈✵♦ ➅➈➇➉

➙ ➛

➜ ➜ ➝ ➜

➜ ➝ ➜ ➝ ➝ ➜

➞ ➟

➞ ➟

➠ ➡ ➢ ➠ ➤

➥ ➡ ➢ ➥ ➦➧

❩♦ ✵❤❡ ▲♦✐❈✵s ♦✺ ✐❈✵❡✹s❡◆✵✐♦❈ ✿✹❡ ➅➨❬ ➩➇ ✿❈❞➅➫➭❬ ➆➈➇❑

➯ ➲

➲

➳ ➵ ➵

➵ ➳

➸ ➺ ➸ ➻➼➽

➺ ➸ ➾ ➻➸➽

➚➪ ➶ ➹

➹ ➪

❩➃❖s✵✐✵➃✵✐❈➄ ➅➆➇ ✐❈✵♦ ➅➈➇➉

➘ ➴

➷ ➬➷ ➬

➮ ➱ ➮ ✃

➱ ➱ ✃

➮ ➱ ✃

✃ ➱ ✃

❐ ❐ ❐

❐ ❐

❐ ❐

❐ ❐

❒ ❮ ❮ ❒ ❮ ❰

Ï ❒ Ð Ñ

Ï Ð Ð Ñ

Ð

ÏÒÓ Ð

Ô

Ô

❩➃❖s✵✐✵➃✵✐❈➄ ✐❈✵♦ ➅➆➇➉

Õ Ö Õ Ö×ØÙ

ÚÛÜÖ Ö×

ØÙÚÛÜÝ Õ

Õ Õ Þ Ö Þ Ý Õ

ß à

ß à

á

âã ä

á

âå

á

âä

äå

æ

áã ä á å á ä á

ç

ç

❩♦ ✵❤❡ s♦è➃✵✐♦❈s ✿✹❡ éêëì

íîï

ð

ñòóô

õ✿❈❞ ➅➆❬ ➆➇❑

ö ÷ ø

ø

ù ù ú ú

ú ù

û ü ý þ ÿ✭✮

ý ÿü✮

✷ ✷✤ � ✤ ✤ ✢

✢ ✤

❩➃❖s✵✐✵➃✵✐❈➄ ➅➈➇ ✐❈✵♦ ➅➆➇➉

✁ ✂ ✁ ✂✄ ☎ ✄ ✄ ✄ ✄ ✛

✄ ☎ ✛

✄ ☎ ✛

① ① ① ①

① ①

① ①

✻ ✆ ✝ ✆ ✆ ✽

✝ ✝✹ ✞✝ ✽

✶✝ ✸✻ ✽

✟ ✟

✟

✟

✿s ✹❡q➃✐✹❡❞❑

❜

✠ ✡

☛ ☞ ✌

☛ ✌

✌

✍ ✍

✍

✍

✎✏ ✑✒ ✵

✒ ✵

✒

✓

✓

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✹ ❚♦�✁✂ ✄☎ ✆✝✁✞✟ ✠✡☛☞✌☛✍✁✂ ✎✡✞✂✍✁♦✞✝ ✍♦ ✝♦✏✑✒ �✌♦✓✏✒✔✝

✣❡r❡ ✕s ✖♥❧② ✖♥❡ ✗✖✕♥t ✖❢ ✕♥t❡rs❡❝t✕✖♥✘✇❤✕❝❤ ✙❡❛♥s t❤❛t t❤❡ ❧✕♥❡ ✕s t❛♥❣❡♥t t✖t❤❡ ❝✕r❝❧❡✳

✻ ✤

✤

✚ ✛①

✚ ① ①

✸ ✜✶✢

✸ ✥ ✜✭✢✷✦ ✧

✦ ★ ✧

❙✉❜st✕t✉t✕♥❣ ✩✪✫ ✕♥t✖ ✩✬✫✮

✯ ✰

✱ ✲ ✴ ✱

✴ ✴ ✱ ✲

✴ ✱ ✱ ✲

♠✵ ✵ ✵

✵ ✵ ♠✵

✵ ♠ ✵

✺ ✺ ✼

✺ ✽ ✾

✺ ✿ ✽ ✾

❀

❀

❀

❖♥❧② ✖♥❡ ✕♥t❡rs❡❝t✕✖♥ ✙❡❛♥s t❤❛t t❤✕sq✉❛❞r❛t✕❝ ❤❛s ❛ s✕♥❣❧❡ r✖✖t✘ s✖ ❁ ❂ ❃✮

❄ ❅

❆ ❇

❆ ❈ ❆ ❉ ❉ ❇

❈ ❇

❈ ❇ ❊

❇ ❆ ❊ ❇ ❆ ❊

❋ ●❍

■

■

■

■

❏ ❑

❬ ▲ ▼◆❪ ❏ P ◗ ❑

▼ ◗❏

▼ ◗❏

▼ ◗❏ ▼ ◗ ❘

❯

❯

❯

❱❲❳❨❩❭❫❳ ❴❵

✐ ❥❡t ✖♥❡ ♥✉✙❜❡r ❜❡ ❦ ❛♥❞ t❤❡ ✖t❤❡r ❜❡ ♣✳

❙✉✙ ✖❢ ❦ ❛♥❞ ♣ ✕s ✈✮ ③④ ⑤ ⑥ ⑦⑧⑨⑩ ❶

❷r✖❞✉❝t ✕s ❸✳❹❺✮ ❻❼❽ ❾❿➀➁ ➂➃➄➅

➆r✖✙ ✩✪✫✮ ➇➈ ➉➊ ➋➌➍➎ ➏

❙✉❜st✕t✉t✕♥❣ ✩➐✫ ✕♥t✖ ✩✬✫✮

➑ ➒

➑ ➒➑ ➒

➓ ➔

➓ → ➔

➓ → ➔

➓ ➓ ➔

➔ ➔

➣ ➣

➣ ➣

➣ ➣

➣ ➣

➣ ➣

↔ ↕➙➛➜

↔➝↕

➞➟

➞ ➝➠ ➝↕ ➟

➠ ➝ ➠ ➡➝ ➟

➝

➠➢➤

➡➝

➠

➥

➥

✣❡ t✇✖ ♥✉✙❜❡rs ❛r❡ ✪✳❺ ❛♥❞ ➦✳❺✳

➧➨➩➩➫➭➯

➲➳ ➵➸ ➺➻➳➼➽ ➾➵➸➼ ➳➺ ➚➺➽➪➼➶➳ ➹➼➚➵➘➴➷➸➬➸➮➚➱ ➴➸ ✃❐❒❮❰ ➵➽➳➺ ➻➶➴➚➳➵➺➽➸ ➳➺ ➘➴Ï➼➸➮Ð➸➼Ñ➮➼➽➳ ➘➴➽➵Ò➮➷➴➳➵➺➽ ➼➴➸➵➼➶❐ Ó➱➼Ñ➮➴➹➶➴➳➵➚ ➚➺➮➷➹ ➴➷➸➺ ➱➴➪➼ Ð➼➼➽ ➸➺➷➪➼➹➾➵➳➱ ➴ ÔÕÖ× ➺➻ ➚➺➮➶➸➼❐

Ø ✣❡ ❧❡♥❣t❤ ✕s ❦Ù ❧❡t t❤❡ ✇✕❞t❤ ❜❡ ♣✳❷❡r✕✙❡t❡r ✖❢ ✪✬✮

Ú ÛÜ Ý

Ü Ý

Ý Þ

ß à

ß à

à ß

á âá

ã

ã

ä å

æ

æ ç

æ ç

è éê

é é

é é

ëìíî

ï

ï ð

ñ✖✙✗❧❡t✕♥❣ t❤❡ sq✉❛r❡✮

ò ó

ô õ õ

ô õ õ ö

÷ ø ø

ø

ù ú û

ü ý

þ

þ

❙✖ t❤❡ ✙❛ÿ✕✙✉✙ ❛r❡❛ ✕s ❸ ❝✙✷ ✩❛♥❞ ✖❝❝✉rs✇❤❡♥ ❦ ❂ ♣ ❂ ➐✘ ✕✳❡✳ ✇❤❡♥ t❤❡ r❡❝t❛♥❣❧❡ ✕s ❛sq✉❛r❡ ✇✕t❤ s✕❞❡ ➐❝✙✫✳

➧➨➩➩➫➭➯

◆➺➳➼ ➳➱➴➳ ➳➱➼ ➽➼�➴➳➵➪➼ ➸➵�➽ ➘➴Ï➼➸ ➳➱➼Ñ➮➴➹➶➴➳➵➚ ➽➼�➴➳➵➪➼ ➸➱➴Ò➼➹× ➾➱➵➚➱ ➶➼➸➮➷➳➸➵➽ ➴ ➘➴✐➵➘➮➘ ➶➴➳➱➼➶ ➳➱➴➽ ➘➵➽➵➘➮➘➳➮➶➽➵➽� Ò➺➵➽➳❐

✸ ❛ ✁❡✇ ❢❡♥❝✕♥❣ r❡q✉✕r❡❞ ✕s ✬❃❃✙✘ s✖

✤ ✂ ✢

✜ ✢ ✤

① ✄

✄ ①

☎ ✆✵ ☎✵✵

☎✆✵ ☎

✝ ✞

✟

✟ ✠

✟ ✠

❆ ✡②

✡ ✡

✡ ✡

☛☞❡✌

✍✎✏ ✍

✍✎✏ ✍✑

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✺✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛

❜ ❈♦♠♣❧❡☞✐✌❣ ☞❤❡ ✍q✉❛r❡✎

✤ ✏ ✏✢✜ ✛✚

✤ ✏ ✏✙✘✗

✖✕✔

✏✙✘✗

✖✕✔

✢

✜✓

✛

✚✒

✤ ✏✙✘✗

✖✕✔

✏

❆ ✑ ✑

✑

✑

✷ ✣✥✦

✷✣✥✦

✷

✣✥✦

✷

✷✣✥✦

✷

✣✥✦

✷

✧

✧ ✧

✧ ✧

★♠❛✩✐♠✉♠ ❛r❡❛ ✪❤❡✌

✫ ✫①✬✭✮

✯✮✯✰✮✱✲ ✳♦r ✪❤✐❝❤

✴ ✵ ✸ ✴② ✹✻✼ ✹✻✼✽

✹✻✼✽✾

✿ ❀ ❇❛❧❧ ✐✍ ❛☞ ❣r♦✉✌❞ ❧❡✈❡❧ ✪❤❡✌ ❁ ❂ ❃❄

❅ ❉

❊ ❋

❊ ❋

❋ ❋ ❋

t t

t t

t t

● ❍■❏ ❑

● ❍■❏ ❑

❑ ▲▼●

❍■❏◆■❖P

◗

❘❙❚❯❱

❚♦ ☞❤❡ ❲❛❧❧ r❡☞✉r✌✍ ☞♦ ☞❤❡ ❣r♦✉✌❞

❛❳❡r ❨❄❩❙ ✍❄

❜ ❇❬ ✍❬♠♠❡☞r❬ ♦✳ ❛ q✉❛❞r❛☞✐❝✲ ♠❛✩✐♠✉♠

❤❡✐❣❤☞ ❘✈❡r☞❡✩❱ ✐✍ ❤❛❧✳✪❛❬ ❲❡☞✪❡❡✌ ☞❤❡

r♦♦☞✍✲ ❭ ❂ ❃ ❛✌❞ ❪❫❴

❵❢❥❄

❦♥

❦

s ❦✇③④

⑤⑥⑦⑧

✇③④

⑤⑥⑦

❦⑧

❦ ❦

⑨

⑩

❶❷

❸❹❺

❻

❸

❸❹❺

❷❸

❸❹❺❸❹❺

❸

❸❹❺

❼❻ ❽❾

❸❹❺

❽❾

❸❹❺❼❹❻❿➀

➁➂➃

➁➂➃

➄

❘❙❚❯❱

➅➆➇➇➈➉➊

➋➌➍➎ ➏➐➑➒➓ ➔➒➎➐ ➌➔→➣ ↔➣➣↕ ➎➐➒→➣➓ ➑➎➍↕➙ ➔➛➜➝ ➐➞ ↔➟ ➏➐➠➡➒➣➢➍↕➙ ➢➌➣ ➎➤➑➔➞➣➥

➦ ❀ ➧❡r✐♠❡☞❡r ♦✳ ❩❃✎

➨ ➩

➫ ➩ ➭

➫ ➩ ➭

➯ ➲

➯➲

➯➲

➳➵

➳➸ ➺➻

➳ ➺➻➸

➳

➼➻➸

➽

➾ ➚➪➶➹

➘➴➷

➾ ➬➪➶➹

➘➴➷

➚

➾ ➬ ➚

➾ ➬

➮ ➱✃✃

✃✃

✃

✃✃ ✃

✃ ✃

❐

❒❮

❒

❰Ï❮

Ð

❮

Ñ

❰Ï❮

Ð

❮

Ñ

❰Ï❐

Ñ❮

Ò

Ò

Ò Ò

Ò

❜ ❯✐✌❞✐✌❣ ☞❤❡ r♦♦☞✍ ♦✳ ☞❤❡ ❛r❡❛

❡✩♣r❡✍✍✐♦✌✎

ÓÔÕÖ

×ØÙÚ

ÓÔÕÖ

×ØÙÚ

Ú Ú

Û Û

Û Û

Û Û

ÜÝÞ

ßà Ý

ÜÝÞ

ßà Ý

Ý áâãäÝ

à

å

❇❬ ☞❤❡ ✍❬♠♠❡☞r❬ ♦✳ ❛ q✉❛❞r❛☞✐❝✲ ☞❤❡

♠❛✩✐♠✉♠ ❛r❡❛ ❘✈❡r☞❡✩❱ ✐✍ ❤❛❧✳✪❛❬

❲❡☞✪❡❡✌ ☞❤❡ r♦♦☞✍✎

æç

è æéê

ëìê

ë

íëê

î

ï❤❡✌ ðñòóô

õ✲

ö ÷

ö ÷øùú

ûüý

ö ÷

ö

þÿ

✤✵✣

✹

✤✵✣

✹

✶�✵

✣

✤✵ ✤✵

✵

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✻ ▼�✁✂✄ ✂✁☎✆�✝☎✞�✟✝ ✠✡☎☛✞�☛✂ ☞

✌✍✎✎✏✑✒

❚✓✔✕ ✖✗✘✙✚ ✛✙✕✗ ✓✛✜✢ ✣✢✢✤ ✕✗✙✜✢✚ ✘✕✔✤✥ ✛●✦✧ ✗★ ✣✩ ✖✗✪✫✙✢✬✔✤✥ ✬✓✢ ✕✭✘✛★✢✮

❝ ■✯ ❆ ✰ ✱✲✲✳

✴ ✵

✴ ✶ ✵

② ②

②②

✸✷✹

✽✺ ✼✷✷

✺

✽✸✷ ✼✷✷ ✷

✾

✾

❯s✐✿❣ ❀❤❡ ❁✉❛❞❂❛❀✐❃ ✯♦❂♠✉❧❛ ❄✐❀❤

❅❇❈

❉✳ ❜ ✰ ❊❋✲ ❛✿❞ ❍ ✰ ✱✲✲❏

❑▲ ◆ ❖

P❖

P

❑

◗❘❙ ❘❙ ❱

❲❳❙❙

❱❨❩❘❲ ❬❭ ❪❫❩❙❴❘❵❢❥

❦

♥❤❡✿ ♣ ♣ qr

♣t ✈✇①③④⑤ ③⑥⑦ ✇①③④

⑧⑨⑧①⑨

♥❤❡✿ ⑩ ⑩ ❶❷

❸ ❹❺❻❼❽❾ ❿❽➀ ❺❻❼❽

➁➂ ❊✱➃➄✱

➅❀❤❡❂❡✯♦❂❡ ❂❡➆❡❃❀ ❛s ➇ ➈ ✲➉➊♦ ➇ ✰ ✱➃➄✱♠ ❛✿❞ ➋ ✰ ➌➄❋➍♠➄

➎ ➏♦❀❛❧ ➐❂♦➑❀ ✰ ➒ ➓ ➒ ➓➔ → ➔➣ ➣ ➣ ➣↔↕↕ ➙ ➙ ➛↕

➜✐✿❞✐✿❣ ❀❤❡ ❂♦♦❀s ♦✯ ❀❤❡ ❀♦❀❛❧ ➐❂♦➑❀✯✉✿❃❀✐♦✿❏

➝ ➞➟ ➠

➠ ➠

➡ ➡

➡ ➡

➢ ➤➥ ➥

➥ ➦➧ ➤➥

➨➩ ❀❤❡ s➩♠♠❡❀❂➩ ♦✯ ❛ ❁✉❛❞❂❛❀✐❃✳ ❀❤❡♠❛➫✐♠✉♠ ❧✐❡s ❤❛❧✯❄❛➩ ➭❡❀❄❡❡✿ ❀❤❡ ❂♦♦❀s✳✐➄❡➄ ❛❀ ➯ ✰ ✱➲➄

✌✍✎✎✏✑✒

❚✓✔✕ ✖✗✘✙✚ ✛✙✕✗ ✓✛✜✢ ✣✢✢✤ ✕✗✙✜✢✚ ✣✩✖✗✪✫✙✢✬✔✤✥ ✬✓✢ ✕✭✘✛★✢✮

➳➵➸➺➻ ➺➸➼➽➵➾➼➚➵➪➾ ➶➹➼➘➚➵➘➺ ➴

➷➬➮➱✃ ❐❒❮❰✃Ï➮Ð❰

Ñ Ò Ó Ô Õ Ó ÔÖ Ö Ö Ö× ØÙ Ú ÛÜÚ ÝÜÞ

ß

à áà á

â ã ä

â ã ä

ä ã ä

å å

å å

å å

æ çè é

ê ë é

ê ìí ë

î

ï Ò ð♦s✐❀✐ñ❡ ❁✉❛❞❂❛❀✐❃✳ s♦ ❀❤❡ ñ❡❂❀❡➫ ✐s ❛♠✐✿✐♠✉♠ ➐♦✐✿❀➄

ß ò✐✿✐♠✉♠ ❛❀ ➅❋✳ ➌➉ ó ô õö ÷ øù ú û üý

➊♦ þ ✰ ❋✳ ❜ ✰ ➌

ÿ ò❛➫✐♠✉♠ ➋✲ñ❛❧✉❡ ✐s ➃➍ó❍ ✰ ➃➍➄ð❛ss❡s ❀❤❂♦✉❣❤ ➅❊✱✳ ✲➉ ❛✿❞ ➅❞✳ ✲➉ ♠❡❛✿s❀❤❛❀ ✐❀s ❂♦♦❀s ❛❂❡ ➇ ✰ ❊✱ ❛✿❞ ➇ ✰ ❞➄✤❡ ❧✐✿❡♦✯ s➩♠♠❡❀❂➩ ✐s ♠✐❞❄❛➩ ➭❡❀❄❡❡✿ ❀❤❡ ❂♦♦❀s✳✐➄❡➄ ❛❀ ➇ ✰ ✱✳ s♦ ❜ ✰ ✱➄

➊✉➭s❀✐❀✉❀✐✿❣ ➇ ✰ ❊✱ ❛✿❞ ➋ ✰ ✲ ✐✿❀♦

� ✁✢ ✂ ✛② ✄ ① ✷ ☎✽✆

❏

✝ ✞✟ ✠ ✠ ✜

✟ ✜

✟ ✠

❛

❛

❛

✵ ✡ ✡ ☛☞

✵ ✌✻ ☛☞

✸

✍

➊♦ þ ✰ ❊❋✳ ❜ ✰ ✱ ❛✿❞ ❍ ✰ ➃➍➄

✹ ❘♦♦❀s ❛❀ ➇ ✰ ❦ ❛✿❞ ➇ ✰ ❦ ✎ ➃ ó❧✐✿❡ ♦✯s➩♠♠❡❀❂➩ ✐s ➇ ✰ ❦ ✎ ✱ ➅♠✐❞❄❛➩ ➭❡❀❄❡❡✿❀❤❡ ❂♦♦❀s➉➄➊♦ ❀❤❡ ➇✲❃♦♦❂❞✐✿❛❀❡ ♦✯ ❀❤❡ ❀✉❂✿✐✿❣ ➐♦✐✿❀✐s ❦ ✎ ✱➄

✺ Ò ❘♦♦❀s ❛❀ ✏✶

✑❛✿❞ ✱✳ s♦

✒ ✓ ✒ ✓✔ ✕✖✚✙

✘✗✣

✥❢ ✦ ✦ ✦✧

★★

✐➄❡➄ ✩ ✪ ✩♣ ✫✬

✭✱ ✭

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✼✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛

❜ ▲✐☞❡ ✌❢ ✍②♠♠❡✎r② ✐✍ ♠✐❞✇✏② ✑❡✎✇❡❡☞

✎❤❡ r✌✌✎✍t ✤

✣ ✒✜✛✚

✙✘✗✤①

✷✓

✷

✷

✸

✹

✔ ✕✲✖✌✌r❞✐☞✏✎❡ ✌❢ ✢ ✐✍✥

✦

✻ ✧ ◆❡❣✏✎✐✈❡ ★✉✏❞r✏✎✐✖ ✩❛ ✐✍ ☞❡❣✏✎✐✈❡

✧ ◆❡❣✏✎✐✈❡ ✪✲✐☞✎❡r✖❡✫✎ ✩❝ ✐✍ ☞❡❣✏✎✐✈❡

✧ ❙✐☞❣❧❡ ✬r❡✫❡✏✎❡❞✭ r✌✌✎ ✩ ✮ ✯✰ ✱✳✴ ✵✺

✧ ▲✐☞❡ ✌❢ ✍②♠♠❡✎r② ✽ ✾✿❀

❁❂✐✍ ✫✌✍✐✎✐✈❡

✩❃ ✐✍ ✫✌✍✐✎✐✈❡ ✬✏✍ ❛ ✐✍ ☞❡❣✏✎✐✈❡✭

❄❅❆❇❈ ❉❊❋●❍

■❏❑▼❖PP◗❘❚ ❯❘P◗❱◗❲❖ ❳❖❨❩❱◗❲❖ ❬❖▼❘

❭

❪

❫ ❴❵❥ ❦♥

♦

♣ q s ③

s ③

④ ⑤ ⑥ ④ ④ ⑤

⑥ ④ ⑤

⑦ ⑦ ⑦

⑦

⑧⑨ ⑩❶ ❶ ❷❶ ⑩❶

❶ ⑧⑨

❸ ❸

❸

❜ ❹r✌♠ ✬✏✭❺ ✎❤❡ ♠✐☞✐♠✉♠ ✈✏❧✉❡ ✌❢

❻ ❼❽ ❽❾❿ ➀➁➂ ✐✍ ➃➄➅

➆❡☞✖❡ ✎❤❡ ♠✏➇✐♠✉♠ ✈✏❧✉❡ ✌❢

➈ ➉➊ ➊

➋

➌ ➋➍ ➎➏➐➑ ➒ ✐✍ ➓➔

➔→

➔

➔→→→➣

↔ ↕★✉✏❧ r✌✌✎✍ ✩➙ ➛ ➄

➜ ➝

➞ ➟

➠ ➞ ➡ ➡ ➟

➞ ➠ ➟

➟➢

➟ ➢

➤ ➥➦

➧ ➧

➧ ➧

➧

➨ ➩

➫ ➨ ➭ ➫ ➩

➯ ➫ ➩

➯ ➲➭

➭➲ ➭ ➭

➳

➳

➳

➵ ◆✌ r❡✏❧ r✌✌✎✍ ✩➙ ➸ ➄

➺ ➻

➺ ➼ ➼ ➻

➺ ➻

➽

➾ ➚➪

➶

➶

➶

➹ ➘

➴ ➹ ➷ ➘

➬➴ ➮ ➘

➱

➷

✃

✃

❐❒ ❮☞❧② ✌☞❡ ❰❡r✌ ✩➙ ➛ ➄

Ï Ð

Ñ Ò

Ñ Ó Ñ Ô Ô Ò

Ó Ñ Ò

Ó Ò Õ

Ò Ñ Õ

Ö ×Ø

Ù

Ù

Ù

Ù

Ú Û

Ü Ý Þßà Ú Þ á Û

Þ Þâ Û

Þ â á

Þ â á

ã

ã

ã

❐❐ q ä✌✌✎✍ ✌❢ å æç è ç éê ëê ë ì íî ✏r❡

ï ð

ï ð

ï ð

ñ ò òó

ñ ò ô

óñ ò

óñ ò

ó ò

õ õ õ õ õ õ

õ õ

õ õ

õ

ö ÷

ø

ö ö

ø

ø

ø

ø

ø

÷ ùú ÷

û û

û

ü ýþ ÿ ✛ ÿ❦ ✶� ✶

❜ ✤ ✁

✢ ✂

✢ ✂✢ ✂

✄ ☎

✙ ✄ ☎

✙ ✄ ☎

✙ ✙ ☎

✙ ✄ ☎

☎ ☎ ✙

✆

✆ ✆

✆ ✆

✆ ✆

✆ ✆

✝✞

✝ ✝ ✝✞

✷ ✷ ✝✞

✷ ✝✺ ✟

✺ ✠ ✟

✺ ✡r ✠

☛ ☛

☛

☛

☛

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✽ ▼�✁✂✄ ✂✁☎✆�✝☎✞�✟✝ ✠✡☎☛✞�☛✂ ☞

▲✌✍✎ ✏✑✒✓✔✕✌✍✓

✶ ❛ ✖ ❙q✉✗r❡ ✘❡r✐✙❡✚❡r ✛ ✥①

✖✖ ❈✐r❝❧❡ ✘❡r✐✙❡✚❡r ✛ ✜✢②

❜ ✤ ✣ ✦ ✣ ✧★ ✩ ★ ✩✹ ✪✫ ✬ ✪✫

✪

✭

✮ ✯

✰ ✱

✰ ✱

✰ ✲✳✴✵

✷✸✺

✱

✰ ✲ ✱ ✱

✰ ✱ ✲ ✱

❆

✻ ✼

✼✼

✼✼

✼

✼ ✼

✾✿❀✾ ♦❁ s❂❃✾✿❀ ✾✿❀✾ ♦❁ ❄❅✿❄❇❀

❉

❊❉

❊❉

❋ ❊❉❉

❋❉

❉

❋❉ ❋ ❊❉ ❋

● ●

●●

● ●●

●

❞ ❈❍✙✘❧❡✚✐■❣ ✚❤❡ ❏q✉✗r❡❑

◆ ❖◆ ❖

◆ ❖◆ ❖

P ◗ ❘◗

◗◗

❚

❯❱

❲

❳❨

P ◗ ❘◗

❩❬❭

❪❫❴

❘◗

❩❬❭

❪❫❴

◗◗

❚

❯❱

❲

❳❨

❵ ❢ ❢

❢

❥

❦❥ ❦

♠

❥ ❦

♥♣

❥ ❥ ❦

❥

❦❥ ❦

❦

❥ ❦

❦

❥ ❦

♥♣

❥ ❥ ❦

t

t t

❙❍ ✚❤❡ ✙✐■✐✙✉✙ ✗r❡✗ ❍❝❝✉r❏ ✈❤❡■ ✇③

④⑤

⑥ ⑤

⑦ ⑧

⑦ ⑧

⑦⑨

⑩❶❷

❸❹❺⑧

⑦

❻

❼❽❾❿❽➀➁➂➃❽ ➄➅ ➆➇❾❽ ➇➀ ❿➇❾❿➈❽

➈❽➀➃➁➉ ➄➅ ➆➇❾❽ ➇➀ ❿➇❾❿➈❽

➁➄➁➂➈ ➈❽➀➃➁➉ ➄➅ ➆➇❾❽➊➋➋➌

➍➎

➏➊➋➋➌

➍➎➐

➎ ➐

➏➊➋➋➌

➐➐➑➋➌➒➓➔→➣

↔↕➙➙➛➜➝

➞➟➠➡ ➠➢➤➠ ➥➠ ➥➦➧➨➠ ➧➡➩➡➦➦➤➫➭ ➠➟ ➦➥➯➲➳➥➵➭ ➠➢➡ ➩➟➧➦➠➤➧➠ ➥➧ ➠➢➡ ➡➸➲➫➡➦➦➥➟➧ ➵➟➫ ➺➤➵➠➡➫ ➩➟➯➲➳➡➠➥➧➻ ➠➢➡ ➦➼➽➤➫➡➾ ➤➦ ➠➢➡ ➼➽➡➦➠➥➟➧ ➤➦➚➦ ➟➧➳➭ ➵➟➫ ➠➢➡ ➪➤➳➽➡ ➟➵ ➶➹➢➡➫➡ ➠➢➡ ➤➫➡➤ ➥➦ ➯➥➧➥➯➥➦➡➘ ➤➧➘ ➧➟➠ ➵➟➫ ➠➢➡ ➤➩➠➽➤➳ ➪➤➳➽➡ ➟➵ ➠➢➤➠ ➯➥➧➥➯➽➯➴

Cambridge University Press978-1-107-57924-8 — Mathematics for the IB Diploma Standard Level Solutions ManualPaul Fannon , Vesna Kadelburg , Ben Woolley , Stephen Ward ExcerptMore Information

www.cambridge.org© in this web service Cambridge University Press

✾✶ �✁✂✄☎✂✆✝✞ ✟✁✠✞✆✝✡✠☛

✷ ❛ ❈☞r ✌ ✍☞s ✎♦s✐t✐♦♥ ✏✑✒✓ ✔ ✤✒✕ ✒✖ ☞♥❞❈☞r ✗ ✍☞s ✎♦s✐t✐♦♥ ✏✒✕ ✘✤✓ ✔ ✙✒✖✚

✛ ✜ ✛ ✜

✢ ✣✥ ✦

✧ ★ ✧ ★

✧ ★ ✧ ★

✩ ✪ ✫ ✪

✩ ✪ ✪ ✫ ✪ ✪

✩ ✪ ✫ ✪

✩ ✪ ✫ ✫ ✪ ✫

✩ ✪ ✫

✬ ✭ ✭ ① ①

✮ ✮

✮ ✮

✮ ✮ ✮ ✮

✮ ✮

✵ ✯✵ ✰✵ ✱✰ ✺✵ ✵

✯✵ ✰✵ ✱✰ ✺✵

✹✵✵ ✯✵✵✵ ✯✰✵✵ ✯✯✰ ✲✵✵ ✲✵✵

✻✯✰ ✯✲✵✵ ✺✹✵✵

✳✳ ✴

✳✳ ✴

✳

✳ ✳

✳ ✳

✳ ✳

✳

❜ ❈♦♠✎❧❡t✐♥❣ t✍❡ sq✉☞r❡✸

✼ ✽✿❀❁

❂❃❄❅

✼ ✽❆❇❉

❊❋●

✽ ❆❇❉

❊❋●

✿

❀❁

❂

❃❄❅

✼ ✽❆❇❉

❊❋●

✽ ❅

✼ ✽❆❇❉

❊❋●

❅

❍ ■ ■

■

■

■

❏❑▲▼▼❏

❑▲◆❖PP

❏❑▲▲◗

❑▲

▲◗

❑▲◆❖PP

❏❑▲▲◗

❑▲▲◗ ◆❖PP

❏❑▲▲◗

❑▲◆❏

❘ ❘

❘ ❘

❘❘

❘

❙♦ ❚❯ ❱❲❳ ☞♥❞✕ s✐♥❝❡ ❨ ❩ ✒✕ ✐t ❬♦❧❧♦✇st✍☞t t✍❡ ♠✐♥✐♠✉♠ ❭☞❧✉❡ ♦❬ ❨ ✐s ❪❦♠✚

❫ ❛ ❴❡rt❡❵ ♦♥ t✍❡ ❢❤☞❵✐s❥✍☞s ♦♥❧② ♦♥❡ r♦♦t✕ s♦ ♣ ✈ ✒✚

③ ④

③ ④

④

⑤ ⑥⑦

⑧

⑧

⑨ ⑩

❶❷ ⑨ ⑩

❸

❹

❜ ❺q✉☞t✐♦♥ ♦❬ ❻rst ❣r☞✎✍ ✐s

❼ ❽❾ ❿ ➀ ❾ ❿➁ ➂ ➂ ➂➃ ➄ ➅➆ ➆

❙♦ ❭❡rt❡❵ ✐s ☞t ✏✙✕ ✒✖✚❙❡❝♦♥❞ ❣r☞✎✍ ✍☞s ❭❡rt❡❵ ☞t ✏✔✑✕ ✤✖✕ s♦

✐ts ❡q✉☞t✐♦♥ ✐s ➇ ➈➉ ➊ ➊➋ ➌ ➍ ➎ ➏➐

➑t ✎☞ss❡s t✍r♦✉❣✍ ✏✙✕ ✒✖➒ s✉➓st✐t✉t✐♥❣✐♥t♦ t✍❡ ❡q✉☞t✐♦♥ ❣✐❭❡s

➔ →➣ ↔ ↔

➣ ↕

➣ ↕

➙

➙

➙

➛ ➜ ➝ ➞

➝➞ ➞

➟

➞

➠

➡ ➢

➤ ➥➦ ➧ ➨ ➩ ➩

➧ ➨ ➩ ➩ ➩

➧ ➨ ➨ ➩

➫ ➭

➭ ➭

➭ ➭

➯

➲➳ ➲

➯

➲➵ ➵ ➲

➯

➲

➵

➲

➳➯

➲

➸

➸

➸

➺ ➻♦r ✐♥t❡rs❡❝t✐♦♥ ♦❬ ➼ ➽ ➾➚ ➪ ➪➶ ➹➘ ☞♥❞

➴ ➷ ➷ ➬➮ ➱ ➱✃

❐

❒

❐

❮✃

❐❰ ✸

Ï ÐÏ Ð

Ñ Ò Ó Ñ Ñ Ò

Ñ Ò Ó Ñ Ñ Ò

Ñ Ò Ó

Ñ Ò Ó

Ñ Ñ Ó

Ó Ó

Ô Ô Ô Ô

Ô Ô Ô Ô

Ô Ô

Ô Ô

Ô Ô

Ô Ô

Õ Ö×

Ø

Ù

Ø

Ú×

Ø

Ø ÛÜ ÙØ Ù Ú×

Õ ÚÕ ÚÙ Ü

Û ×Û ×Ú Ü

Û Ù Û Ü

Ù

ÛÝÞ Û

ß ß

ß ß

ß

ß

❢ ✈ ✙ ✐s t✍❡ ✎♦✐♥t ♦❬ ✐♥t❡rs❡❝t✐♦♥ ☞t t✍❡❭❡rt❡❵ ✏✙✕ ✒✖ ♦❬ t✍❡ ❻rst ❣r☞✎✍✚

à♦ ❻♥❞ t✍❡ á❤❝♦♦r❞✐♥☞t❡ ♦❬ t✍❡ ♦t✍❡r

✎♦✐♥t✕ s✉➓st✐t✉t❡ âãä

å✐♥t♦ æ çè éê ë ì í✸

î ïðñò

óôõ

îö÷

øø

ùú

û

ü

❙♦ t✍❡ ♦t✍❡r ✎♦✐♥t ♦❬ ✐♥t❡rs❡❝t✐♦♥ ✐s

ýþÿ

✜✛✚

✹

✸✱✷�

✾✚